Numerical differentiation of implicitly defined curves

Muhammed I. Syam, Hani I. Siyyam

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


In this paper we develop a finite differencing device to calculate approximations of derivatives c′(0),c″(0),... of regular solution curves c:R∋s→c(s)∈Rn of nonlinear systems of equations f(x)=0,f∈Ck(Rn+1,Rn) without having to compute points on the solution curve c(s). The derivative vectors c′(0),c″(0),... can be used in the numerical approximation of the solution set f-1(0) to construct higher-order predictors to be used in the predictor-corrector continuation method.

Original languageEnglish
Pages (from-to)131-144
Number of pages14
JournalJournal of Computational and Applied Mathematics
Issue number1-2
Publication statusPublished - Aug 15 1999


  • Continuation method
  • Implicitly defined curve* Higher order predictor
  • Numerical differentiation

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'Numerical differentiation of implicitly defined curves'. Together they form a unique fingerprint.

Cite this